世界上最難的簡單幾何題
你只能使用初等幾何原理來解這道題，也就是說只能使用三角形的內角總和是180度；等腰和等邊三角形的特性；平行線的對頂角相等；全等三角形的角邊角、邊角邊、邊邊邊定理以及三角形相似的角角角定理這一類的基礎知識。不能使用正弦餘弦定理。關於能使用的定理會在下文給出。
這是我所見過的最難的數學題，儘管看起來是如此的簡單。並且真的可以只用初等幾何解題。
Using only elementary geometry, determine angle x. Provide a step-by-step proof.
You may only use elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use more advanced trigonomery, such as the law of sines, the law of cosines, etc. There is a review of elementary geometry below.
This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry. This is not a trick question.
這裡有一個小提示。
Triangle Problem 1 Scale Diagram
Your working diagram should be large and accurate. Draw the diagram yourself using a protractor or print this correctly scaled diagram.
這裡還有另一個小提示。
Triangle Problem 1 Small Hint
To solve the problem, you will need to draw a few more lines inside the triangle.
You will need to do more than merely adding and subtracting angles.
The solution has more steps than you might expect.
這道題排行第二
World's Second-Hardest Easy Geometry Problem
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僅能使用初等幾何原理得出角X的值。並寫出詳細步驟。 這道題是上一題的變形，但是要解出來也絕非易事。 Using only elementary geometry, determine angle x. Provide a step-by-step proof. This is a variation of the problem above. This is also a very hard problem that is, in a sense, easy.
這裡有一個小提示。 |
Triangle Problem 2 Scale Diagram
Your working diagram should be large and accurate. Draw the diagram yourself using a protractor or print this correctly scaled diagram.
這裡還有另一個小提示。
Triangle Problem 2 Small Hint
To solve the problem, you will need to draw a few more lines inside the triangle.
You will need to do more than merely adding and subtracting angles.
The solution has more steps than you might expect.
Problem 2 is not solved in the same way as problem 1.
基礎幾何原理
關於解題你所能用的原理。
相交線和交角：兩條相交線，對角相等，兩個鄰角相加為180度。兩條平行線與第三條線相交，相對的角相等。
三角形：三角形的內角總和是180度。等腰三角形有兩條邊相等，且有兩個相等角。等邊三角形三條邊相等，三個角相等。直角三角形有一個九十度的角。兩個三角形的形狀相似，則它們的對應角相等。
- 邊角邊：有兩邊和它的夾角對應相等的兩個三角形全等
- 邊邊邊：三邊對應相等的兩個三角形全等
- 角邊角：兩個角和兩角夾的邊對應相等的三角形全等
- 角角：如果兩個三角形的兩個對應角相等，那麼這兩個三角形相似
